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- W2952685668 abstract "Let $F(G)$ and $b(G)$ respectively denote the Fitting subgroup and the largest degree of an irreducible complex character of a finite group $G$. A well-known conjecture of D. Gluck claims that if $G$ is solvable then $|G:F(G)|leq b(G)^{2}$. We confirm this conjecture in the case where $|F(G)|$ is coprime to 6. We also extend the problem to arbitrary finite groups and prove several results showing that the largest irreducible character degree of a finite group strongly controls the group structure." @default.
- W2952685668 created "2019-06-27" @default.
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- W2952685668 date "2014-02-03" @default.
- W2952685668 modified "2023-10-16" @default.
- W2952685668 title "On a conjecture of Gluck" @default.
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